Take-home Exercise 3: Geographical Weighted Regression (GWR) analysis of resale prices of public housing in Singapore

This exercise aims to to explain factors affecting the resale prices of public housing in Singapore by building hedonic pricing model using appropriate Geographical Weighted Regression (GWR) methods.

Niharika Avula https://example.com/norajones
2021-11-08

1.0 OVERVIEW

1.1 ABOUT AIRBNB

1.2 PROBLEM STATEMENT

This exercise aims to investigate factors affecting the resale prices of four-room public housing in Singapore by building hedonic pricing models. The hedonic price models will be built using appropriate Geographical Weighted Regression (GWR) methods and by the end of this exercise, the following will be covered:

2.0 GETTING STARTED

This section covers installing the applicable R packages as well as importing the necessary data for analysis

2.1 SETTING UP THE ENVIRONMENT

The following R packages will be used in this analysis:

packages = c('olsrr', 'corrplot', 'ggpubr', 'sf', 'spdep', 'GWmodel', 'tmap', 'tidyverse', 'onemapsgapi', 'dplyr', 'httr', 'rjson')
for (p in packages){
  if(!require(p, character.only = T)){
    install.packages(p)
  }
  library(p,character.only = T)
}

2.2 IMPORTING DATA

The table below shows all the data that will be imported for this analysis

Data Type Name Source
Geospatial Master Plan 2014 Subzone Boundary (Web) link
Aspatial HDB Resale Prices link
Geospatial Childcare OnemapAPI
Geospatial Hawker OnemapAPI
Geospatial Supermarket OnemapAPI
Geospatial MRT & LRT Locations link

DATA TALKING POINTS:

2.2.1 IMPORTING GEOSPATIAL DATA

Master Plan 2014 Subzone Boundary

mpsz <- st_read(dsn = "data/geospatial", 
                   layer = "MP14_SUBZONE_WEB_PL")
Reading layer `MP14_SUBZONE_WEB_PL' from data source 
  `C:\Niharika-avula\IS415_blog\_posts\Take Home Exercise- 3\data\geospatial' 
  using driver `ESRI Shapefile'
Simple feature collection with 323 features and 15 fields
Geometry type: MULTIPOLYGON
Dimension:     XY
Bounding box:  xmin: 2667.538 ymin: 15748.72 xmax: 56396.44 ymax: 50256.33
Projected CRS: SVY21

SUPERMARKET

Importing this data from OnemapAPI using the code chunk below

supermarket <- st_read("data/geospatial/supermarkets-geojson.geojson")%>%
  mutate(lat = st_coordinates(.)[,2], lng = st_coordinates(.)[,1])%>%
  st_transform(crs = 3414)
Reading layer `supermarkets-geojson' from data source 
  `C:\Niharika-avula\IS415_blog\_posts\Take Home Exercise- 3\data\geospatial\supermarkets-geojson.geojson' 
  using driver `GeoJSON'
Simple feature collection with 526 features and 2 fields
Geometry type: POINT
Dimension:     XYZ
Bounding box:  xmin: 103.6258 ymin: 1.24715 xmax: 104.0036 ymax: 1.461526
z_range:       zmin: 0 zmax: 0
Geodetic CRS:  WGS 84
glimpse(supermarket)
Rows: 526
Columns: 5
$ Name        <chr> "kml_1", "kml_2", "kml_3", "kml_4", "kml_5", "km~
$ Description <chr> "<center><table><tr><th colspan='2' align='cente~
$ geometry    <POINT [m]> POINT Z (35561.22 42685.17 0), POINT Z (32~
$ lat         <dbl> 1.402303, 1.314239, 1.373321, 1.332959, 1.353453~
$ lng         <dbl> 103.9013, 103.8709, 103.8864, 103.9149, 103.9530~

HAWKER CENTRES

hawker <- st_read("data/geospatial/hawker-centres-geojson.geojson")%>%
  mutate(lat = st_coordinates(.)[,2], lng = st_coordinates(.)[,1])%>% 
  st_transform(crs = 3414)
Reading layer `hawker-centres-geojson' from data source 
  `C:\Niharika-avula\IS415_blog\_posts\Take Home Exercise- 3\data\geospatial\hawker-centres-geojson.geojson' 
  using driver `GeoJSON'
Simple feature collection with 125 features and 2 fields
Geometry type: POINT
Dimension:     XYZ
Bounding box:  xmin: 103.6974 ymin: 1.272716 xmax: 103.9882 ymax: 1.449217
z_range:       zmin: 0 zmax: 0
Geodetic CRS:  WGS 84
glimpse(hawker)
Rows: 125
Columns: 5
$ Name        <chr> "kml_1", "kml_2", "kml_3", "kml_4", "kml_5", "km~
$ Description <chr> "<center><table><tr><th colspan='2' align='cente~
$ geometry    <POINT [m]> POINT Z (39731.49 34910.13 0), POINT Z (26~
$ lat         <dbl> 1.331987, 1.287331, 1.372385, 1.363157, 1.352007~
$ lng         <dbl> 103.9387, 103.8183, 103.8290, 103.8667, 103.8370~

CHILDCARE

childcare <- st_read("data/geospatial/child-care-services-geojson.geojson")%>%
  mutate(lat = st_coordinates(.)[,2], lng = st_coordinates(.)[,1])%>%
  st_transform(crs = 3414)
Reading layer `child-care-services-geojson' from data source 
  `C:\Niharika-avula\IS415_blog\_posts\Take Home Exercise- 3\data\geospatial\child-care-services-geojson.geojson' 
  using driver `GeoJSON'
Simple feature collection with 1545 features and 2 fields
Geometry type: POINT
Dimension:     XYZ
Bounding box:  xmin: 103.6824 ymin: 1.248403 xmax: 103.9897 ymax: 1.462134
z_range:       zmin: 0 zmax: 0
Geodetic CRS:  WGS 84
glimpse(childcare)
Rows: 1,545
Columns: 5
$ Name        <chr> "kml_1", "kml_2", "kml_3", "kml_4", "kml_5", "km~
$ Description <chr> "<center><table><tr><th colspan='2' align='cente~
$ geometry    <POINT [m]> POINT Z (27976.73 45716.7 0), POINT Z (258~
$ lat         <dbl> 1.429720, 1.286680, 1.354655, 1.386540, 1.319731~
$ lng         <dbl> 103.8331, 103.8138, 103.8639, 103.8447, 103.9521~

MRT & LRT

MRT_LRT <- st_read(dsn = "data/geospatial", 
                   layer = "MRTLRTStnPtt")
Reading layer `MRTLRTStnPtt' from data source 
  `C:\Niharika-avula\IS415_blog\_posts\Take Home Exercise- 3\data\geospatial' 
  using driver `ESRI Shapefile'
Simple feature collection with 171 features and 3 fields
Geometry type: POINT
Dimension:     XY
Bounding box:  xmin: 6138.311 ymin: 27555.06 xmax: 45254.86 ymax: 47854.2
Projected CRS: SVY21

2.2.3 IMPORTING ASPATIAL DATA

HDB_resale <- read_csv("data/aspatial/HDB resale-flat-prices.csv", show_col_types=FALSE)

We have come to end of Section 2 with R packages installed and the Geospatial and Aspatial data imported, next section will cover data wrangling process of the imported data

3.0 GEOSPATIAL DATA WRANGLING

This section covers all the steps taken in the pre-processing of the mpsz data, which includes the following steps:

Took reference from senior’s project given as sample for this section

3.1 HANDLING MISSING VALUES

Checking for missing values as they can impact future calculations and visualisations.

Master Plan 2014 Subzone Boundary

mpsz[rowSums(is.na(mpsz))!=0,]
Simple feature collection with 0 features and 15 fields
Bounding box:  xmin: NA ymin: NA xmax: NA ymax: NA
Projected CRS: SVY21
 [1] OBJECTID   SUBZONE_NO SUBZONE_N  SUBZONE_C  CA_IND     PLN_AREA_N
 [7] PLN_AREA_C REGION_N   REGION_C   INC_CRC    FMEL_UPD_D X_ADDR    
[13] Y_ADDR     SHAPE_Leng SHAPE_Area geometry  
<0 rows> (or 0-length row.names)

There are no missing values in both mpsz data

SUPERMARKET

supermarket[rowSums(is.na(supermarket))!=0,]
Simple feature collection with 0 features and 4 fields
Bounding box:  xmin: NA ymin: NA xmax: NA ymax: NA
Projected CRS: SVY21 / Singapore TM
[1] Name        Description geometry    lat         lng        
<0 rows> (or 0-length row.names)

There are no missing values in both supermarket data

HAWKER CENTRES

hawker[rowSums(is.na(hawker))!=0,]
Simple feature collection with 0 features and 4 fields
Bounding box:  xmin: NA ymin: NA xmax: NA ymax: NA
Projected CRS: SVY21 / Singapore TM
[1] Name        Description geometry    lat         lng        
<0 rows> (or 0-length row.names)

There are no missing values in both hawker data

CHILDCARE

childcare[rowSums(is.na(childcare))!=0,]
Simple feature collection with 0 features and 4 fields
Bounding box:  xmin: NA ymin: NA xmax: NA ymax: NA
Projected CRS: SVY21 / Singapore TM
[1] Name        Description geometry    lat         lng        
<0 rows> (or 0-length row.names)

There are no missing values in both childcare data

MRT & LRT

MRT_LRT[rowSums(is.na(MRT_LRT))!=0,]
Simple feature collection with 0 features and 3 fields
Bounding box:  xmin: NA ymin: NA xmax: NA ymax: NA
Projected CRS: SVY21
[1] OBJECTID STN_NAME STN_NO   geometry
<0 rows> (or 0-length row.names)

There are no missing values in both MRT_LRT data

3.2 HANDLING INVALID GEOMETRIES

Checking for invalid geometries as they can impact future calculations and visualisations.

Master Plan 2014 Subzone Boundary

length(which(st_is_valid(mpsz) == FALSE))
[1] 9

It can be seen that there are 9 invalid geometries in the mpsz data, hence the invalid geometries need to be made valid

mpsz <- st_make_valid(mpsz)
length(which(st_is_valid(mpsz) == FALSE))
[1] 0

Invalid geometries have been handled, there are no more invalid geometries in above dataset.

SUPERMARKET

length(which(st_is_valid(supermarket) == FALSE))
[1] 0

It can be seen that there are no invalid geometries in the supermarket data

HAWKER CENTRES

length(which(st_is_valid(hawker) == FALSE))
[1] 0

It can be seen that there are no invalid geometries in the hawker data

CHILDCARE

length(which(st_is_valid(childcare) == FALSE))
[1] 0

It can be seen that there are no invalid geometries in the childcare data

MRT & LRT
length(which(st_is_valid(MRT_LRT) == FALSE))
[1] 0

It can be seen that there are no invalid geometries in the MRT_LRT data

3.3 VERIFYING & TRANSFORMING CRS

Master Plan 2014 Subzone Boundary

st_crs(mpsz) 
Coordinate Reference System:
  User input: SVY21 
  wkt:
PROJCRS["SVY21",
    BASEGEOGCRS["SVY21[WGS84]",
        DATUM["World Geodetic System 1984",
            ELLIPSOID["WGS 84",6378137,298.257223563,
                LENGTHUNIT["metre",1]],
            ID["EPSG",6326]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["Degree",0.0174532925199433]]],
    CONVERSION["unnamed",
        METHOD["Transverse Mercator",
            ID["EPSG",9807]],
        PARAMETER["Latitude of natural origin",1.36666666666667,
            ANGLEUNIT["Degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",103.833333333333,
            ANGLEUNIT["Degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["Scale factor at natural origin",1,
            SCALEUNIT["unity",1],
            ID["EPSG",8805]],
        PARAMETER["False easting",28001.642,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",38744.572,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["(E)",east,
            ORDER[1],
            LENGTHUNIT["metre",1,
                ID["EPSG",9001]]],
        AXIS["(N)",north,
            ORDER[2],
            LENGTHUNIT["metre",1,
                ID["EPSG",9001]]]]

It can be seen that while the projected CRS is SVY21, the current EPSG Code is 9001, hence the next step is to assign the correct 3414 EPSG code

mpsz <- st_set_crs(mpsz, 3414)
st_crs(mpsz) 
Coordinate Reference System:
  User input: EPSG:3414 
  wkt:
PROJCRS["SVY21 / Singapore TM",
    BASEGEOGCRS["SVY21",
        DATUM["SVY21",
            ELLIPSOID["WGS 84",6378137,298.257223563,
                LENGTHUNIT["metre",1]]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["degree",0.0174532925199433]],
        ID["EPSG",4757]],
    CONVERSION["Singapore Transverse Mercator",
        METHOD["Transverse Mercator",
            ID["EPSG",9807]],
        PARAMETER["Latitude of natural origin",1.36666666666667,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",103.833333333333,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["Scale factor at natural origin",1,
            SCALEUNIT["unity",1],
            ID["EPSG",8805]],
        PARAMETER["False easting",28001.642,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",38744.572,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["northing (N)",north,
            ORDER[1],
            LENGTHUNIT["metre",1]],
        AXIS["easting (E)",east,
            ORDER[2],
            LENGTHUNIT["metre",1]],
    USAGE[
        SCOPE["Cadastre, engineering survey, topographic mapping."],
        AREA["Singapore - onshore and offshore."],
        BBOX[1.13,103.59,1.47,104.07]],
    ID["EPSG",3414]]

SUPERMARKET

st_crs(supermarket)
Coordinate Reference System:
  User input: EPSG:3414 
  wkt:
PROJCRS["SVY21 / Singapore TM",
    BASEGEOGCRS["SVY21",
        DATUM["SVY21",
            ELLIPSOID["WGS 84",6378137,298.257223563,
                LENGTHUNIT["metre",1]]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["degree",0.0174532925199433]],
        ID["EPSG",4757]],
    CONVERSION["Singapore Transverse Mercator",
        METHOD["Transverse Mercator",
            ID["EPSG",9807]],
        PARAMETER["Latitude of natural origin",1.36666666666667,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",103.833333333333,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["Scale factor at natural origin",1,
            SCALEUNIT["unity",1],
            ID["EPSG",8805]],
        PARAMETER["False easting",28001.642,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",38744.572,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["northing (N)",north,
            ORDER[1],
            LENGTHUNIT["metre",1]],
        AXIS["easting (E)",east,
            ORDER[2],
            LENGTHUNIT["metre",1]],
    USAGE[
        SCOPE["Cadastre, engineering survey, topographic mapping."],
        AREA["Singapore - onshore and offshore."],
        BBOX[1.13,103.59,1.47,104.07]],
    ID["EPSG",3414]]

The correct projected CRS with EPSG Code 3413 is assigned

HAWKER CENTRES

st_crs(hawker)
Coordinate Reference System:
  User input: EPSG:3414 
  wkt:
PROJCRS["SVY21 / Singapore TM",
    BASEGEOGCRS["SVY21",
        DATUM["SVY21",
            ELLIPSOID["WGS 84",6378137,298.257223563,
                LENGTHUNIT["metre",1]]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["degree",0.0174532925199433]],
        ID["EPSG",4757]],
    CONVERSION["Singapore Transverse Mercator",
        METHOD["Transverse Mercator",
            ID["EPSG",9807]],
        PARAMETER["Latitude of natural origin",1.36666666666667,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",103.833333333333,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["Scale factor at natural origin",1,
            SCALEUNIT["unity",1],
            ID["EPSG",8805]],
        PARAMETER["False easting",28001.642,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",38744.572,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["northing (N)",north,
            ORDER[1],
            LENGTHUNIT["metre",1]],
        AXIS["easting (E)",east,
            ORDER[2],
            LENGTHUNIT["metre",1]],
    USAGE[
        SCOPE["Cadastre, engineering survey, topographic mapping."],
        AREA["Singapore - onshore and offshore."],
        BBOX[1.13,103.59,1.47,104.07]],
    ID["EPSG",3414]]

The correct projected CRS with EPSG Code 3413 is assigned

CHILDCARE

st_crs(childcare)
Coordinate Reference System:
  User input: EPSG:3414 
  wkt:
PROJCRS["SVY21 / Singapore TM",
    BASEGEOGCRS["SVY21",
        DATUM["SVY21",
            ELLIPSOID["WGS 84",6378137,298.257223563,
                LENGTHUNIT["metre",1]]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["degree",0.0174532925199433]],
        ID["EPSG",4757]],
    CONVERSION["Singapore Transverse Mercator",
        METHOD["Transverse Mercator",
            ID["EPSG",9807]],
        PARAMETER["Latitude of natural origin",1.36666666666667,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",103.833333333333,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["Scale factor at natural origin",1,
            SCALEUNIT["unity",1],
            ID["EPSG",8805]],
        PARAMETER["False easting",28001.642,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",38744.572,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["northing (N)",north,
            ORDER[1],
            LENGTHUNIT["metre",1]],
        AXIS["easting (E)",east,
            ORDER[2],
            LENGTHUNIT["metre",1]],
    USAGE[
        SCOPE["Cadastre, engineering survey, topographic mapping."],
        AREA["Singapore - onshore and offshore."],
        BBOX[1.13,103.59,1.47,104.07]],
    ID["EPSG",3414]]

The correct projected CRS with EPSG Code 3413 is assigned

MRT & LRT

st_crs(MRT_LRT)
Coordinate Reference System:
  User input: SVY21 
  wkt:
PROJCRS["SVY21",
    BASEGEOGCRS["SVY21[WGS84]",
        DATUM["World Geodetic System 1984",
            ELLIPSOID["WGS 84",6378137,298.257223563,
                LENGTHUNIT["metre",1]],
            ID["EPSG",6326]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["Degree",0.0174532925199433]]],
    CONVERSION["unnamed",
        METHOD["Transverse Mercator",
            ID["EPSG",9807]],
        PARAMETER["Latitude of natural origin",1.36666666666667,
            ANGLEUNIT["Degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",103.833333333333,
            ANGLEUNIT["Degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["Scale factor at natural origin",1,
            SCALEUNIT["unity",1],
            ID["EPSG",8805]],
        PARAMETER["False easting",28001.642,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",38744.572,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["(E)",east,
            ORDER[1],
            LENGTHUNIT["metre",1,
                ID["EPSG",9001]]],
        AXIS["(N)",north,
            ORDER[2],
            LENGTHUNIT["metre",1,
                ID["EPSG",9001]]]]

It can be seen that while the projected CRS is SVY21, the current EPSG Code is 9001, hence the next step is to assign the correct 3414 EPSG code

MRT_LRT <- st_set_crs(MRT_LRT, 3414)
st_crs(MRT_LRT) 
Coordinate Reference System:
  User input: EPSG:3414 
  wkt:
PROJCRS["SVY21 / Singapore TM",
    BASEGEOGCRS["SVY21",
        DATUM["SVY21",
            ELLIPSOID["WGS 84",6378137,298.257223563,
                LENGTHUNIT["metre",1]]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["degree",0.0174532925199433]],
        ID["EPSG",4757]],
    CONVERSION["Singapore Transverse Mercator",
        METHOD["Transverse Mercator",
            ID["EPSG",9807]],
        PARAMETER["Latitude of natural origin",1.36666666666667,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",103.833333333333,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["Scale factor at natural origin",1,
            SCALEUNIT["unity",1],
            ID["EPSG",8805]],
        PARAMETER["False easting",28001.642,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",38744.572,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["northing (N)",north,
            ORDER[1],
            LENGTHUNIT["metre",1]],
        AXIS["easting (E)",east,
            ORDER[2],
            LENGTHUNIT["metre",1]],
    USAGE[
        SCOPE["Cadastre, engineering survey, topographic mapping."],
        AREA["Singapore - onshore and offshore."],
        BBOX[1.13,103.59,1.47,104.07]],
    ID["EPSG",3414]]

The correct projected CRS with EPSG Code 3413 is assigned

VISUALISING GEOSPATIAL DATA

Before we jump into the analysis, it is a good practice to visualise the geospatial data

tmap_mode("view")
tm_shape(mpsz) +
  tm_borders(alpha = 0.5) +
  tmap_options(check.and.fix = TRUE) +

tm_shape(MRT_LRT) +
  tm_dots(col = 'red', size = 0.02) +
  
tm_shape(supermarket) +
  tm_dots(col = 'black', size = 0.02) +
  
tm_shape(childcare) +
  tm_dots(col = 'green', size = 0.02) +
  
tm_shape(hawker) +
  tm_dots(col = 'blue', size = 0.02) 
tmap_mode("plot")

4.0 ASPATIAL DATA WRANGLING

This section covers all the steps taken to extract the data based on focus area, convert the street name and block number to derive the postal code followed by the pre-processing of the HDB_resale data, which includes the following steps:

Let’s have a glimpse at the data first

glimpse(HDB_resale)
Rows: 111,706
Columns: 11
$ month               <chr> "2017-01", "2017-01", "2017-01", "2017-0~
$ town                <chr> "ANG MO KIO", "ANG MO KIO", "ANG MO KIO"~
$ flat_type           <chr> "2 ROOM", "3 ROOM", "3 ROOM", "3 ROOM", ~
$ block               <chr> "406", "108", "602", "465", "601", "150"~
$ street_name         <chr> "ANG MO KIO AVE 10", "ANG MO KIO AVE 4",~
$ storey_range        <chr> "10 TO 12", "01 TO 03", "01 TO 03", "04 ~
$ floor_area_sqm      <dbl> 44, 67, 67, 68, 67, 68, 68, 67, 68, 67, ~
$ flat_model          <chr> "Improved", "New Generation", "New Gener~
$ lease_commence_date <dbl> 1979, 1978, 1980, 1980, 1980, 1981, 1979~
$ remaining_lease     <chr> "61 years 04 months", "60 years 07 month~
$ resale_price        <dbl> 232000, 250000, 262000, 265000, 265000, ~

It can be seen that there is no geometry data and the address is given as street name and block number instead, therefore onemapAPI will be used to derive the postal code and geometry data, but before that let’s extract the data of four-room houses within the specific period.

4.1 Extracting sub dataset in HDB_resale

As we are only interested in four-room houses transacted from 1st January 2019 to 30th September 2020, we have to extract this from the HDB_resale data which contains infromation since 2017 and for all flat types

HDB_resale_four_room <- filter(HDB_resale, flat_type == '4 ROOM')
glimpse(HDB_resale_four_room)
Rows: 46,467
Columns: 11
$ month               <chr> "2017-01", "2017-01", "2017-01", "2017-0~
$ town                <chr> "ANG MO KIO", "ANG MO KIO", "ANG MO KIO"~
$ flat_type           <chr> "4 ROOM", "4 ROOM", "4 ROOM", "4 ROOM", ~
$ block               <chr> "472", "475", "629", "546", "131", "254"~
$ street_name         <chr> "ANG MO KIO AVE 10", "ANG MO KIO AVE 10"~
$ storey_range        <chr> "10 TO 12", "07 TO 09", "01 TO 03", "01 ~
$ floor_area_sqm      <dbl> 92, 91, 94, 92, 98, 97, 92, 91, 92, 97, ~
$ flat_model          <chr> "New Generation", "New Generation", "New~
$ lease_commence_date <dbl> 1979, 1979, 1981, 1981, 1979, 1977, 1979~
$ remaining_lease     <chr> "61 years 06 months", "61 years 06 month~
$ resale_price        <dbl> 400000, 400000, 403000, 410000, 425888, ~

It can be seen that the flat-type is filtered to contain only 4 Room flats, next step is to further filter based on the transaction period but the data type of month column is in character.

dates_to_include <- c('2019-01', '2019-02', '2019-03', '2019-04', '2019-05', '2019-06', '2019-07', '2019-08', '2019-09', '2019-10', '2019-11', '2019-12', '2020-01', '2020-02', '2020-03', '2020-04', '2020-05', '2020-06', '2020-07', '2020-08', '2020-09')
HDB_resale_filtered <- filter(HDB_resale_four_room, month %in% dates_to_include)
glimpse(HDB_resale_filtered)
Rows: 15,901
Columns: 11
$ month               <chr> "2019-01", "2019-01", "2019-01", "2019-0~
$ town                <chr> "ANG MO KIO", "ANG MO KIO", "ANG MO KIO"~
$ flat_type           <chr> "4 ROOM", "4 ROOM", "4 ROOM", "4 ROOM", ~
$ block               <chr> "204", "175", "543", "118", "411", "546"~
$ street_name         <chr> "ANG MO KIO AVE 3", "ANG MO KIO AVE 4", ~
$ storey_range        <chr> "01 TO 03", "07 TO 09", "01 TO 03", "04 ~
$ floor_area_sqm      <dbl> 92, 91, 92, 99, 92, 92, 92, 92, 93, 91, ~
$ flat_model          <chr> "New Generation", "New Generation", "New~
$ lease_commence_date <dbl> 1977, 1981, 1981, 1978, 1979, 1981, 1978~
$ remaining_lease     <chr> "57 years", "61 years 06 months", "61 ye~
$ resale_price        <dbl> 330000, 360000, 370000, 375000, 380000, ~

With this, the subset data we are interested in is extracted for further analysis and has 15901 rows

4.2 Pre-Processing HDB_resale

4.2.1 Extracting LAT & LNG from OnemapAPI

As a first step, a new column will be created with the block and street name combined and this columns will be used to search for the geometry data from onemapAPI

library(stringr)
HDB_resale_filtered$block_street <- str_c(HDB_resale_filtered$block, ' ', HDB_resale_filtered$street_name)
HDB_resale_filtered$block_street <- gsub(" ", "+", HDB_resale_filtered$block_street, fixed = TRUE)
glimpse(HDB_resale_filtered)
Rows: 15,901
Columns: 12
$ month               <chr> "2019-01", "2019-01", "2019-01", "2019-0~
$ town                <chr> "ANG MO KIO", "ANG MO KIO", "ANG MO KIO"~
$ flat_type           <chr> "4 ROOM", "4 ROOM", "4 ROOM", "4 ROOM", ~
$ block               <chr> "204", "175", "543", "118", "411", "546"~
$ street_name         <chr> "ANG MO KIO AVE 3", "ANG MO KIO AVE 4", ~
$ storey_range        <chr> "01 TO 03", "07 TO 09", "01 TO 03", "04 ~
$ floor_area_sqm      <dbl> 92, 91, 92, 99, 92, 92, 92, 92, 93, 91, ~
$ flat_model          <chr> "New Generation", "New Generation", "New~
$ lease_commence_date <dbl> 1977, 1981, 1981, 1978, 1979, 1981, 1978~
$ remaining_lease     <chr> "57 years", "61 years 06 months", "61 ye~
$ resale_price        <dbl> 330000, 360000, 370000, 375000, 380000, ~
$ block_street        <chr> "204+ANG+MO+KIO+AVE+3", "175+ANG+MO+KIO+~

The following function is written to extract the geometry data (Source: Link)

library(onemapsgapi)
library(httr)
getcoordinates <- function(address){
  query_string <-str_c('https://developers.onemap.sg/commonapi/search?searchVal=', toString(address), '&returnGeom=Y&getAddrDetails=Y&pageNum=1')
  jsonresp <- GET(query_string)
  resp <- content(jsonresp, as="parsed")
  if (length(resp$results) != 0){
    
    resp_df <- resp$results
    resp_df_final <- resp_df%>%bind_rows%>%select(BLK_NO, ROAD_NAME, POSTAL, X, Y, LATITUDE, LONGTITUDE)
    #print(resp_df_final)
  }
  else{
    resp_df_final <- 0
  }
  
  return(resp_df_final)
}

Using for loop, all 15901 addresses are passed to extract the geometry data

HDB_resale_filtered$Lat <- 0
HDB_resale_filtered$Lng <- 0

for (x in HDB_resale_filtered$block_street) {
  index <- match(x, HDB_resale_filtered$block_street)
  F_results <- as.list(getcoordinates(x))
  if(length(F_results$LATITUDE)!=0){
    HDB_resale_filtered$Lat[index] <- F_results$LATITUDE
  }
  else
  {
    HDB_resale_filtered$Lat[index] <- NA
  }
  
  if(length(F_results$LONGTITUDE)!=0){
    HDB_resale_filtered$Lng[index] <- F_results$LONGTITUDE
  }
  else
  {
    HDB_resale_filtered$Lng[index] <- NA
  }
  
  }

Displaying the dataset

head(HDB_resale_filtered)
# A tibble: 6 x 14
  month   town       flat_type block street_name storey_range floor_area_sqm
  <chr>   <chr>      <chr>     <chr> <chr>       <chr>                 <dbl>
1 2019-01 ANG MO KIO 4 ROOM    204   ANG MO KIO~ 01 TO 03                 92
2 2019-01 ANG MO KIO 4 ROOM    175   ANG MO KIO~ 07 TO 09                 91
3 2019-01 ANG MO KIO 4 ROOM    543   ANG MO KIO~ 01 TO 03                 92
4 2019-01 ANG MO KIO 4 ROOM    118   ANG MO KIO~ 04 TO 06                 99
5 2019-01 ANG MO KIO 4 ROOM    411   ANG MO KIO~ 04 TO 06                 92
6 2019-01 ANG MO KIO 4 ROOM    546   ANG MO KIO~ 10 TO 12                 92
# ... with 7 more variables: flat_model <chr>,
#   lease_commence_date <dbl>, remaining_lease <chr>,
#   resale_price <dbl>, block_street <chr>, Lat <chr>, Lng <chr>

Lat and Lng values are appended correctly and now we can move on to the next step of wrangling process to convert the CRS and handle any missing values

4.2.2 Handling Missing Values

sum(is.na(HDB_resale_filtered$Lng))
[1] 13
sum(is.na(HDB_resale_filtered$Lat))
[1] 13

Therefore, there are 13 missing values which could be not obtained due to API error, so we can proceed to remove them.

HDB_resale_filtered <- HDB_resale_filtered[!(is.na(HDB_resale_filtered$Lng)), ]
HDB_resale_filtered <- HDB_resale_filtered[!(is.na(HDB_resale_filtered$Lat)), ]

4.2.2 Converting into sf objects and transforming the Coordinate system

HDB_resale_filtered_sf <- st_as_sf(HDB_resale_filtered, 
                      coords = c("Lng", 
                                 "Lat"), 
                      crs=4326) %>%
  st_transform(crs = 3414)

st_crs(HDB_resale_filtered_sf)
Coordinate Reference System:
  User input: EPSG:3414 
  wkt:
PROJCRS["SVY21 / Singapore TM",
    BASEGEOGCRS["SVY21",
        DATUM["SVY21",
            ELLIPSOID["WGS 84",6378137,298.257223563,
                LENGTHUNIT["metre",1]]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["degree",0.0174532925199433]],
        ID["EPSG",4757]],
    CONVERSION["Singapore Transverse Mercator",
        METHOD["Transverse Mercator",
            ID["EPSG",9807]],
        PARAMETER["Latitude of natural origin",1.36666666666667,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",103.833333333333,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["Scale factor at natural origin",1,
            SCALEUNIT["unity",1],
            ID["EPSG",8805]],
        PARAMETER["False easting",28001.642,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",38744.572,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["northing (N)",north,
            ORDER[1],
            LENGTHUNIT["metre",1]],
        AXIS["easting (E)",east,
            ORDER[2],
            LENGTHUNIT["metre",1]],
    USAGE[
        SCOPE["Cadastre, engineering survey, topographic mapping."],
        AREA["Singapore - onshore and offshore."],
        BBOX[1.13,103.59,1.47,104.07]],
    ID["EPSG",3414]]

Done, it is correctly assigned now.

4.3 Processing Locational Factors

The locational factors used in this analysis are as below which will be calculated in this section:

Deriving Proximity AND frequency count of locational factors

FOR PROXIMITY MEASURE: Instead of using the Onemapsgapi wrapper as suggested due to its limitations such as high time consumption and loss of data due to API error, another function called the st_distance() from sf will be used, the source of this code chunk is from the link shown here. (Source: LINK)

FOR FREQUENCY COUNT: For the purpose of this, I will considering the frequency count of the supermarkets etc WITHIN 1km radius which seems more realistic

The code chunk below is written to calculate the distance and frequency for each of the different locational factors

SUPERMARKET

library(units)
library(matrixStats)
radius <- 1000
HDB_resale_filtered_sf$Prox_supermarket <- 0
HDB_resale_filtered_sf$Freq_supermarket <- 0
dist1 <- st_distance(HDB_resale_filtered_sf, supermarket) 
dist1 <- drop_units(dist1)
HDB_resale_filtered_sf$Prox_supermarket <-round(rowMins(dist1))
dist1_df <- as.data.frame(dist1)
HDB_resale_filtered_sf$Freq_supermarket <- rowSums(dist1_df <= radius)

HAWKER CENTRES

radius <- 1000
HDB_resale_filtered_sf$Prox_hawker <- 0
HDB_resale_filtered_sf$Freq_hawker <- 0
dist2 <- st_distance(HDB_resale_filtered_sf, hawker)
dist2 <- drop_units(dist2)
HDB_resale_filtered_sf$Prox_hawker <- round(rowMins(dist2))
dist2_df <- as.data.frame(dist2)
HDB_resale_filtered_sf$Freq_hawker <- rowSums(dist2_df <= radius)

CHILDCARE

radius <- 1000
HDB_resale_filtered_sf$Prox_childcare <- 0
HDB_resale_filtered_sf$Freq_childcare <- 0
dist3 <- st_distance(HDB_resale_filtered_sf, childcare)
dist3 <- drop_units(dist3)
HDB_resale_filtered_sf$Prox_childcare <- round(rowMins(dist3))
dist3_df <- as.data.frame(dist3)
HDB_resale_filtered_sf$Freq_childcare <- rowSums(dist3_df <= radius)

MRT & LRT

Frequency of MRT and LRT stations is not applicable

HDB_resale_filtered_sf$Prox_MRT_LRT <- 0
dist4 <- st_distance(HDB_resale_filtered_sf, MRT_LRT)
dist4 <- drop_units(dist4)
HDB_resale_filtered_sf$Prox_MRT_LRT <- round(rowMins(dist4))
glimpse(HDB_resale_filtered_sf)
Rows: 15,888
Columns: 20
$ month               <chr> "2019-01", "2019-01", "2019-01", "2019-0~
$ town                <chr> "ANG MO KIO", "ANG MO KIO", "ANG MO KIO"~
$ flat_type           <chr> "4 ROOM", "4 ROOM", "4 ROOM", "4 ROOM", ~
$ block               <chr> "204", "175", "543", "118", "411", "546"~
$ street_name         <chr> "ANG MO KIO AVE 3", "ANG MO KIO AVE 4", ~
$ storey_range        <chr> "01 TO 03", "07 TO 09", "01 TO 03", "04 ~
$ floor_area_sqm      <dbl> 92, 91, 92, 99, 92, 92, 92, 92, 93, 91, ~
$ flat_model          <chr> "New Generation", "New Generation", "New~
$ lease_commence_date <dbl> 1977, 1981, 1981, 1978, 1979, 1981, 1978~
$ remaining_lease     <chr> "57 years", "61 years 06 months", "61 ye~
$ resale_price        <dbl> 330000, 360000, 370000, 375000, 380000, ~
$ block_street        <chr> "204+ANG+MO+KIO+AVE+3", "175+ANG+MO+KIO+~
$ geometry            <POINT [m]> POINT (29179.92 38822.08), POINT (~
$ Prox_supermarket    <dbl> 271, 310, 319, 459, 338, 313, 309, 380, ~
$ Freq_supermarket    <dbl> 7, 4, 3, 4, 4, 3, 6, 4, 1, 1, 7, 8, 6, 1~
$ Prox_hawker         <dbl> 442, 270, 258, 436, 70, 299, 229, 343, 2~
$ Freq_hawker         <dbl> 5, 4, 2, 4, 3, 2, 5, 5, 2, 2, 3, 5, 5, 2~
$ Prox_childcare      <dbl> 191, 135, 80, 190, 175, 159, 134, 73, 12~
$ Freq_childcare      <dbl> 25, 19, 14, 18, 17, 13, 25, 19, 20, 15, ~
$ Prox_MRT_LRT        <dbl> 704, 403, 890, 201, 887, 921, 501, 363, ~

With this, we have all the proximity leasures of the locational factors

4.3 Processing Structural Factors

Structural factors being considered are as follows: * Area of Unit * Remaining Lease

str(HDB_resale_filtered_sf)
sf [15,888 x 20] (S3: sf/tbl_df/tbl/data.frame)
 $ month              : chr [1:15888] "2019-01" "2019-01" "2019-01" "2019-01" ...
 $ town               : chr [1:15888] "ANG MO KIO" "ANG MO KIO" "ANG MO KIO" "ANG MO KIO" ...
 $ flat_type          : chr [1:15888] "4 ROOM" "4 ROOM" "4 ROOM" "4 ROOM" ...
 $ block              : chr [1:15888] "204" "175" "543" "118" ...
 $ street_name        : chr [1:15888] "ANG MO KIO AVE 3" "ANG MO KIO AVE 4" "ANG MO KIO AVE 10" "ANG MO KIO AVE 4" ...
 $ storey_range       : chr [1:15888] "01 TO 03" "07 TO 09" "01 TO 03" "04 TO 06" ...
 $ floor_area_sqm     : num [1:15888] 92 91 92 99 92 92 92 92 93 91 ...
 $ flat_model         : chr [1:15888] "New Generation" "New Generation" "New Generation" "New Generation" ...
 $ lease_commence_date: num [1:15888] 1977 1981 1981 1978 1979 ...
 $ remaining_lease    : chr [1:15888] "57 years" "61 years 06 months" "61 years 01 month" "58 years 04 months" ...
 $ resale_price       : num [1:15888] 330000 360000 370000 375000 380000 380000 385000 395000 395000 395000 ...
 $ block_street       : chr [1:15888] "204+ANG+MO+KIO+AVE+3" "175+ANG+MO+KIO+AVE+4" "543+ANG+MO+KIO+AVE+10" "118+ANG+MO+KIO+AVE+4" ...
 $ geometry           :sfc_POINT of length 15888; first list element:  'XY' num [1:2] 29180 38822
 $ Prox_supermarket   : num [1:15888] 271 310 319 459 338 313 309 380 693 779 ...
 $ Freq_supermarket   : num [1:15888] 7 4 3 4 4 3 6 4 1 1 ...
 $ Prox_hawker        : num [1:15888] 442 270 258 436 70 299 229 343 217 556 ...
 $ Freq_hawker        : num [1:15888] 5 4 2 4 3 2 5 5 2 2 ...
 $ Prox_childcare     : num [1:15888] 191 135 80 190 175 159 134 73 125 116 ...
 $ Freq_childcare     : num [1:15888] 25 19 14 18 17 13 25 19 20 15 ...
 $ Prox_MRT_LRT       : num [1:15888] 704 403 890 201 887 921 501 363 571 543 ...
 - attr(*, "sf_column")= chr "geometry"
 - attr(*, "agr")= Factor w/ 3 levels "constant","aggregate",..: NA NA NA NA NA NA NA NA NA NA ...
  ..- attr(*, "names")= chr [1:19] "month" "town" "flat_type" "block" ...

It can be seen that remaining_lease is in character type and needs to be converted

HDB_resale_filtered_sf$remaining_lease <- as.numeric(gsub(".*?([0-9]+).*", "\\1", HDB_resale_filtered_sf$remaining_lease)) 
str(HDB_resale_filtered_sf)
sf [15,888 x 20] (S3: sf/tbl_df/tbl/data.frame)
 $ month              : chr [1:15888] "2019-01" "2019-01" "2019-01" "2019-01" ...
 $ town               : chr [1:15888] "ANG MO KIO" "ANG MO KIO" "ANG MO KIO" "ANG MO KIO" ...
 $ flat_type          : chr [1:15888] "4 ROOM" "4 ROOM" "4 ROOM" "4 ROOM" ...
 $ block              : chr [1:15888] "204" "175" "543" "118" ...
 $ street_name        : chr [1:15888] "ANG MO KIO AVE 3" "ANG MO KIO AVE 4" "ANG MO KIO AVE 10" "ANG MO KIO AVE 4" ...
 $ storey_range       : chr [1:15888] "01 TO 03" "07 TO 09" "01 TO 03" "04 TO 06" ...
 $ floor_area_sqm     : num [1:15888] 92 91 92 99 92 92 92 92 93 91 ...
 $ flat_model         : chr [1:15888] "New Generation" "New Generation" "New Generation" "New Generation" ...
 $ lease_commence_date: num [1:15888] 1977 1981 1981 1978 1979 ...
 $ remaining_lease    : num [1:15888] 57 61 61 58 59 61 58 62 60 60 ...
 $ resale_price       : num [1:15888] 330000 360000 370000 375000 380000 380000 385000 395000 395000 395000 ...
 $ block_street       : chr [1:15888] "204+ANG+MO+KIO+AVE+3" "175+ANG+MO+KIO+AVE+4" "543+ANG+MO+KIO+AVE+10" "118+ANG+MO+KIO+AVE+4" ...
 $ geometry           :sfc_POINT of length 15888; first list element:  'XY' num [1:2] 29180 38822
 $ Prox_supermarket   : num [1:15888] 271 310 319 459 338 313 309 380 693 779 ...
 $ Freq_supermarket   : num [1:15888] 7 4 3 4 4 3 6 4 1 1 ...
 $ Prox_hawker        : num [1:15888] 442 270 258 436 70 299 229 343 217 556 ...
 $ Freq_hawker        : num [1:15888] 5 4 2 4 3 2 5 5 2 2 ...
 $ Prox_childcare     : num [1:15888] 191 135 80 190 175 159 134 73 125 116 ...
 $ Freq_childcare     : num [1:15888] 25 19 14 18 17 13 25 19 20 15 ...
 $ Prox_MRT_LRT       : num [1:15888] 704 403 890 201 887 921 501 363 571 543 ...
 - attr(*, "sf_column")= chr "geometry"
 - attr(*, "agr")= Factor w/ 3 levels "constant","aggregate",..: NA NA NA NA NA NA NA NA NA NA ...
  ..- attr(*, "names")= chr [1:19] "month" "town" "flat_type" "block" ...

With that, we can conclude the data wrangling process and proceed to the next section

5.0 Exploratory Data Analysis

5.1 Histogram Plots - Distribution of variables

The distribution of the independent variables is shown using histogram

AREA_SQM <- ggplot(data=HDB_resale_filtered_sf, aes(x= `floor_area_sqm`)) +
  geom_histogram(bins=20, color="black", fill="light blue")

Remaining_Lease <- ggplot(data=HDB_resale_filtered_sf, aes(x= `remaining_lease`)) +
  geom_histogram(bins=20, color="black", fill="light blue")

Prox_supermarket1 <- ggplot(data=HDB_resale_filtered_sf, aes(x= `Prox_supermarket`)) +
  geom_histogram(bins=20, color="black", fill="light blue") +
  xlim(0, 3000)

Prox_hawker1 <- ggplot(data=HDB_resale_filtered_sf, aes(x= `Prox_hawker`)) +
  geom_histogram(bins=20, color="black", fill="light blue")+
  xlim(0, 3000)

Prox_childcare1 <- ggplot(data=HDB_resale_filtered_sf, aes(x= `Prox_childcare`)) +
  geom_histogram(bins=20, color="black", fill="light blue")+
  xlim(0, 1000)
  
Prox_MRT_LRT1 <- ggplot(data=HDB_resale_filtered_sf, aes(x= `Prox_MRT_LRT`)) +
  geom_histogram(bins=20, color="black", fill="light blue")+
  xlim(0, 3000)

Freq_supermarket <- ggplot(data=HDB_resale_filtered_sf, aes(x= `Freq_supermarket`)) +
  geom_histogram(bins=20, color="black", fill="light blue")

Freq_hawker <- ggplot(data=HDB_resale_filtered_sf, aes(x= `Freq_hawker`)) +
  geom_histogram(bins=20, color="black", fill="light blue")

Freq_childcare <- ggplot(data=HDB_resale_filtered_sf, aes(x= `Freq_childcare`)) +
  geom_histogram(bins=20, color="black", fill="light blue")

ggarrange(AREA_SQM, Remaining_Lease, Prox_supermarket1, Prox_hawker1, Prox_childcare1, Prox_MRT_LRT1, Freq_supermarket, Freq_hawker, Freq_childcare)

5.2 Statistical Point Map

Now, we will be plotting the geospatial distribution HDB resale prices in Singapore
tmap_mode("view")
tm_shape(mpsz)+
  tm_polygons() +
tm_shape(HDB_resale_filtered_sf) +  
  tm_dots(col = "resale_price",
          alpha = 0.6,
          style="quantile")
tmap_mode("plot")

6.0 Hedonic Pricing Modelling

In this section, the following two models will be covered: * Multiple Linear Regression Method * GWmodel

6.1 Multiple Linear Regression Method

6.1.1 Removing Unused columns

The code chunk below is used to remove unused columns
HDB_resale_final <- subset(HDB_resale_filtered_sf, select = -c(block_street, lease_commence_date, flat_model))
str(HDB_resale_final)
sf [15,888 x 17] (S3: sf/tbl_df/tbl/data.frame)
 $ month           : chr [1:15888] "2019-01" "2019-01" "2019-01" "2019-01" ...
 $ town            : chr [1:15888] "ANG MO KIO" "ANG MO KIO" "ANG MO KIO" "ANG MO KIO" ...
 $ flat_type       : chr [1:15888] "4 ROOM" "4 ROOM" "4 ROOM" "4 ROOM" ...
 $ block           : chr [1:15888] "204" "175" "543" "118" ...
 $ street_name     : chr [1:15888] "ANG MO KIO AVE 3" "ANG MO KIO AVE 4" "ANG MO KIO AVE 10" "ANG MO KIO AVE 4" ...
 $ storey_range    : chr [1:15888] "01 TO 03" "07 TO 09" "01 TO 03" "04 TO 06" ...
 $ floor_area_sqm  : num [1:15888] 92 91 92 99 92 92 92 92 93 91 ...
 $ remaining_lease : num [1:15888] 57 61 61 58 59 61 58 62 60 60 ...
 $ resale_price    : num [1:15888] 330000 360000 370000 375000 380000 380000 385000 395000 395000 395000 ...
 $ geometry        :sfc_POINT of length 15888; first list element:  'XY' num [1:2] 29180 38822
 $ Prox_supermarket: num [1:15888] 271 310 319 459 338 313 309 380 693 779 ...
 $ Freq_supermarket: num [1:15888] 7 4 3 4 4 3 6 4 1 1 ...
 $ Prox_hawker     : num [1:15888] 442 270 258 436 70 299 229 343 217 556 ...
 $ Freq_hawker     : num [1:15888] 5 4 2 4 3 2 5 5 2 2 ...
 $ Prox_childcare  : num [1:15888] 191 135 80 190 175 159 134 73 125 116 ...
 $ Freq_childcare  : num [1:15888] 25 19 14 18 17 13 25 19 20 15 ...
 $ Prox_MRT_LRT    : num [1:15888] 704 403 890 201 887 921 501 363 571 543 ...
 - attr(*, "sf_column")= chr "geometry"
 - attr(*, "agr")= Factor w/ 3 levels "constant","aggregate",..: NA NA NA NA NA NA NA NA NA NA ...
  ..- attr(*, "names")= chr [1:16] "month" "town" "flat_type" "block" ...

6.1.2 Building Multiple linear regression method

HDB.mlr <- lm(formula = resale_price ~ floor_area_sqm+remaining_lease+Prox_supermarket+Prox_hawker+Prox_childcare+Prox_MRT_LRT+Freq_supermarket+Freq_hawker+Freq_childcare,data=HDB_resale_final)
summary(HDB.mlr)

Call:
lm(formula = resale_price ~ floor_area_sqm + remaining_lease + 
    Prox_supermarket + Prox_hawker + Prox_childcare + Prox_MRT_LRT + 
    Freq_supermarket + Freq_hawker + Freq_childcare, data = HDB_resale_final)

Residuals:
    Min      1Q  Median      3Q     Max 
-206108  -72186  -27206   40382  712943 

Coefficients:
                  Estimate Std. Error t value Pr(>|t|)    
(Intercept)      86145.655  15292.055   5.633 1.80e-08 ***
floor_area_sqm     812.367    122.949   6.607 4.04e-11 ***
remaining_lease   3585.982     68.847  52.087  < 2e-16 ***
Prox_supermarket   -38.222      9.252  -4.131 3.63e-05 ***
Prox_hawker         10.509      3.461   3.036  0.00240 ** 
Prox_childcare      74.985      9.869   7.598 3.17e-14 ***
Prox_MRT_LRT       -47.272      4.117 -11.481  < 2e-16 ***
Freq_supermarket  2082.758    680.960   3.059  0.00223 ** 
Freq_hawker      39946.605   1341.389  29.780  < 2e-16 ***
Freq_childcare   -2503.516    192.347 -13.016  < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 106200 on 15878 degrees of freedom
Multiple R-squared:  0.2193,    Adjusted R-squared:  0.2189 
F-statistic: 495.7 on 9 and 15878 DF,  p-value: < 2.2e-16

With reference to the report above, it is clear that not all the independent variables are statistically significant at 1%. I will investigate further by removing those variables which are not statistically significant at 1%.

Therefore removing Prox_hawker and Freq_supermarket from the model

HDB.mlr1 <- lm(formula = resale_price ~ floor_area_sqm+remaining_lease+Prox_supermarket+Prox_childcare+Prox_MRT_LRT+Freq_hawker+Freq_childcare,data=HDB_resale_final)
summary(HDB.mlr1)

Call:
lm(formula = resale_price ~ floor_area_sqm + remaining_lease + 
    Prox_supermarket + Prox_childcare + Prox_MRT_LRT + Freq_hawker + 
    Freq_childcare, data = HDB_resale_final)

Residuals:
    Min      1Q  Median      3Q     Max 
-207438  -72522  -27808   40376  712950 

Coefficients:
                   Estimate Std. Error t value Pr(>|t|)    
(Intercept)      100772.108  14878.064   6.773 1.30e-11 ***
floor_area_sqm      829.182    122.740   6.756 1.47e-11 ***
remaining_lease    3587.814     68.818  52.135  < 2e-16 ***
Prox_supermarket    -40.638      9.038  -4.496 6.96e-06 ***
Prox_childcare       88.060      9.340   9.428  < 2e-16 ***
Prox_MRT_LRT        -47.423      4.118 -11.516  < 2e-16 ***
Freq_hawker       38649.271   1069.503  36.138  < 2e-16 ***
Freq_childcare    -2249.090    172.111 -13.068  < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 106300 on 15880 degrees of freedom
Multiple R-squared:  0.2185,    Adjusted R-squared:  0.2182 
F-statistic: 634.3 on 7 and 15880 DF,  p-value: < 2.2e-16

However, there is no significant change in the adjust R squared value and hence I will be using all of the variables.

HDB.mlr <- lm(formula = resale_price ~ floor_area_sqm+remaining_lease+Prox_supermarket+Prox_hawker+Prox_childcare+Prox_MRT_LRT+Freq_supermarket+Freq_hawker+Freq_childcare,data=HDB_resale_final)
ols_regress(HDB.mlr)
                             Model Summary                              
-----------------------------------------------------------------------
R                       0.468       RMSE                    106200.739 
R-Squared               0.219       Coef. Var                   24.494 
Adj. R-Squared          0.219       MSE                11278596988.483 
Pred R-Squared          0.219       MAE                      78549.360 
-----------------------------------------------------------------------
 RMSE: Root Mean Square Error 
 MSE: Mean Square Error 
 MAE: Mean Absolute Error 

                                     ANOVA                                       
--------------------------------------------------------------------------------
                    Sum of                                                      
                   Squares           DF        Mean Square       F         Sig. 
--------------------------------------------------------------------------------
Regression    5.031854e+13            9       5.590949e+12    495.713    0.0000 
Residual      1.790816e+14        15878    11278596988.483                      
Total         2.294001e+14        15887                                         
--------------------------------------------------------------------------------

                                          Parameter Estimates                                            
--------------------------------------------------------------------------------------------------------
           model         Beta    Std. Error    Std. Beta       t        Sig         lower         upper 
--------------------------------------------------------------------------------------------------------
     (Intercept)    86145.655     15292.055                   5.633    0.000    56171.493    116119.817 
  floor_area_sqm      812.367       122.949        0.048      6.607    0.000      571.372      1053.362 
 remaining_lease     3585.982        68.847        0.383     52.087    0.000     3451.035      3720.929 
Prox_supermarket      -38.222         9.252    -3563.579     -4.131    0.000      -56.357       -20.086 
     Prox_hawker       10.509         3.461      979.764      3.036    0.002        3.724        17.293 
  Prox_childcare       74.985         9.869     6991.364      7.598    0.000       55.640        94.329 
    Prox_MRT_LRT      -47.272         4.117    -4407.490    -11.481    0.000      -55.343       -39.202 
Freq_supermarket     2082.758       680.960        0.057      3.059    0.002      748.000      3417.516 
     Freq_hawker    39946.605      1341.389        0.341     29.780    0.000    37317.331     42575.879 
  Freq_childcare    -2503.516       192.347       -0.252    -13.016    0.000    -2880.537     -2126.494 
--------------------------------------------------------------------------------------------------------

6.1.3 Checking for multicolinearity

It is important to ensure that the independent variables used are not highly correlated to each other as the quality of the model will be compromised, therefore the correlation matrix is plotted below.

ols_vif_tol(HDB.mlr)
         Variables    Tolerance          VIF
1   floor_area_sqm 9.314229e-01 1.073626e+00
2  remaining_lease 9.083126e-01 1.100943e+00
3 Prox_supermarket 6.607015e-11 1.513543e+10
4      Prox_hawker 4.720553e-10 2.118396e+09
5   Prox_childcare 5.806922e-11 1.722083e+10
6     Prox_MRT_LRT 3.336179e-10 2.997441e+09
7 Freq_supermarket 1.421302e-01 7.035802e+00
8      Freq_hawker 3.746472e-01 2.669178e+00
9   Freq_childcare 1.315021e-01 7.604439e+00

Since the VIF of the independent variables are more than 10 for the four proximity measures. there seems to be multicollinearity among those independent variables.

6.1.4 Test for Non-Linearity

ols_plot_resid_fit(HDB.mlr)

The figure above reveals that most some of the data points are scattered far above the 0 line, hence there could be relationships between the dependent variable and independent variables which are not linear.

6.1.4 Test for Normality Assumption

ols_plot_resid_hist(HDB.mlr)

The figure reveals that the residual of the multiple linear regression model is skewed to the right.

6.1.4 Test for Spatial Autocorrelation

First, export the residual of the hedonic pricing model and save it as a data frame.

mlr.output <- as.data.frame(HDB.mlr$residuals)

Next, we will join the newly created data frame with HDB_resale_filtered_sf object.

HDB_resale.res.sf <- cbind(HDB_resale_final, 
                        HDB.mlr$residuals) %>%
rename(`MLR_RES` = `HDB.mlr.residuals`)

Next, convert the simple feature object into a SpatialPointsDataFrame

HDB_resale.sp <- as_Spatial(HDB_resale.res.sf)
HDB_resale.sp
class       : SpatialPointsDataFrame 
features    : 15888 
extent      : -13597396, 42623.63, 28217.39, 19891558  (xmin, xmax, ymin, ymax)
crs         : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs 
variables   : 17
names       :   month,       town, flat_type, block,   street_name, storey_range, floor_area_sqm, remaining_lease, resale_price, Prox_supermarket, Freq_supermarket, Prox_hawker, Freq_hawker, Prox_childcare, Freq_childcare, ... 
min values  : 2019-01, ANG MO KIO,    4 ROOM,     1,  ADMIRALTY DR,     01 TO 03,             74,              45,       218000,                0,                0,          33,           0,              0,              0, ... 
max values  : 2020-09,     YISHUN,    4 ROOM,    9B, YUNG SHENG RD,     49 TO 51,            138,              97,      1186888,         24067427,               16,    24068164,           9,       24068061,             59, ... 

Next, use tmap package to display the distribution of the residuals on an interactive map.

tmap_mode("view")
tm_shape(mpsz)+
  tm_polygons(alpha = 0.4) +
tm_shape(HDB_resale.res.sf) +  
  tm_dots(col = "MLR_RES",
          alpha = 0.6,
          style="quantile") 
tmap_mode("plot")

Moran’s I test

nb <- dnearneigh(coordinates(HDB_resale.sp), 0, 1500, longlat = FALSE)
summary(nb)
Neighbour list object:
Number of regions: 15888 
Number of nonzero links: 118517906 
Percentage nonzero weights: 46.95107 
Average number of links: 7459.586 
1 region with no links:
3088
Link number distribution:

    0     2     3     9    10    11    14    19    21    22    23 
    1     1     3     5     4     1    15     2     1    23     1 
   24    25    26    27    28    29    30    31    32    33    34 
    3     1     2     1     1     6     3     6     5    11     6 
   35    36    37    38    39    40    41    42    43    44    45 
    1     3     7     4    10     3     2    12     4     5     1 
   47    48    49    50    51    52    53    54    55    56    57 
    4     7     3     5     7     5    10     9     7    10     5 
   58    59    60    61    62    63    64    65    66    67    68 
    7     8     3    17    13    15    29    13    19    15    13 
   69    70    71    72    73    74    75    76    77    78    79 
    8    16    12    16    11    12    11    16    10    12    19 
   80    81    82    83    84    85    86    87    88    89    90 
   21    18    12    16     8    11     4     8    25    21    18 
   91    92    93    94    95    96    97    98    99   100   101 
   23    20    15    13    19    13    24    21    15    15    17 
  102   103   104   105   106   107   108   109   110   111   112 
   30    10    24    21    25    22    23    29    32    14    42 
  113   114   115   116   117   118   119   120   121   122   123 
   20    17    23    17    43    19    23    22    19    30    28 
  124   125   126   127   128   129   130   131   132   133   134 
   20    12    20    18    22    24    16    39    23    28    16 
  135   136   137   138   139   140   141   142   143   144   145 
   19    31    18    29    19    15    20    20    27    19    15 
  146   147   148   149   150   151   152   153   154   155   156 
   35    19    18    23    19    17    23    24    17    23    19 
  157   158   159   160   161   162   163   164   165   166   167 
   22    17    15    11    26    16    13    14    19    19    19 
  168   169   170   171   172   173   174   175   176   177   178 
   16    14    15    19    22    18    18     8    14    19     9 
  179   180   181   182   183   184   185   186   187   188   189 
   18    18    20    15    21    14    11    22    19    21    16 
  190   191   192   193   194   195   196   197   198   199   200 
   20    23    27    14    16    15    20    24    25    11    17 
  201   202   203   204   205   206   207   208   209   210   211 
   23    21    21    32    15    24    24    19    26    20    23 
  212   213   214   215   216   217   218   219   220   221   222 
   31    21    23    16    19    24    28    11    28    20    25 
  223   224   225   226   227   228   229   230   231   232   233 
   28    21    26    14    17    34    24    14    23    19    19 
  234   235   236   237   238   239   240   241   242   243   244 
   18    26    17    14    21    17    15     9    16    15    10 
  245   246   247   248   249   250   251   252   253   254   255 
   14    17    14    17    29    16    21    13    18    13    28 
  256   257   258   259   260   261   262   263   264   265   266 
   12    18     8    11    20    16    17    18    14    11    13 
  267   268   269   270   271   272   273   274   275   276   277 
    8    15    12    10     7    15    10    13    14    30    14 
  278   279   280   281   282   283   284   285   286   287   288 
   12    11     5     5     4    10     5     8     9     8     6 
  289   290   291   292   293   294   295   296   297   298   299 
    9     5     6     6     8    12     7     5    10     9     8 
  300   301   302   303   304   305   306   307   308   309   310 
    4     6     7     5    11     6    12     8     9     8    11 
  311   312   313   314   315   316   317   318   319   320   321 
   10    12     7     6     4     9     4    10     3     8    11 
  322   323   324   325   326   327   328   329   330   331   332 
    5     9     8     7     5     7     8     8     6    10     5 
  333   334   335   336   337   338   339   340   341   342   343 
    8     6    12     4     4     3    10     4     5     5    10 
  344   345   346   347   348   349   350   351   352   353   354 
    9     7     8     8     6     3     9     3     4     7     6 
  355   356   357   358   359   360   361   362   363   364   365 
    6     3     4     3     8     3     5     1     5     5     7 
  366   367   368   369   370   371   372   373   374   375   376 
    3     1     5     5     6     4     4     3     2     3     2 
  377   378   380   381   382   383   384   385   386   387   388 
    3     2     3     3     1     3     2     2     3     1     3 
  389   390   392   394   395   396   397   398   400   401   402 
    2     2     2     3     4     1     1     1     2     2     2 
  404   405   407   408   412   413   415   416   417   418   423 
    1     3     1     1     2     1     5     2     1     1     1 
  424   425   428   430   431   433   434   438   441   443   444 
    1     1     2     1     1     1     2     2     1     1     2 
  445   448   453   454   455   457   464   467   470   473   474 
    1     1     1     1     1     1     1     1     1     1     1 
10843 
10844 
1 least connected region:
13294 with 2 links
10844 most connected regions:
54 87 91 97 129 135 141 145 171 184 185 193 200 201 203 205 216 258 267 286 294 296 333 337 344 348 352 354 357 358 366 368 397 398 401 403 416 425 426 427 430 436 440 444 445 455 457 486 495 502 520 522 536 540 558 565 566 577 591 592 595 623 641 643 644 645 648 650 652 656 658 661 669 677 680 681 698 700 704 712 713 716 719 724 732 741 745 749 752 760 761 766 768 769 770 771 777 784 796 798 801 815 818 822 827 829 836 845 846 847 850 851 856 857 865 869 870 877 893 899 908 910 926 928 953 959 962 965 966 969 972 973 976 979 987 992 995 1008 1011 1026 1029 1030 1031 1032 1033 1034 1038 1039 1043 1046 1047 1048 1051 1052 1058 1062 1071 1072 1102 1103 1110 1112 1116 1119 1123 1128 1130 1140 1141 1154 1163 1174 1181 1185 1187 1188 1190 1191 1192 1198 1200 1202 1211 1220 1227 1228 1229 1231 1235 1236 1240 1244 1246 1247 1248 1253 1256 1257 1258 1267 1272 1274 1276 1278 1279 1280 1282 1284 1287 1288 1289 1291 1298 1303 1304 1305 1307 1309 1311 1312 1317 1318 1321 1335 1337 1343 1345 1348 1349 1350 1351 1353 1356 1357 1359 1361 1366 1368 1374 1375 1378 1382 1383 1384 1387 1388 1392 1394 1399 1401 1402 1403 1413 1414 1415 1424 1426 1427 1429 1431 1441 1444 1451 1457 1458 1461 1466 1469 1471 1472 1475 1483 1484 1486 1491 1498 1503 1508 1512 1521 1522 1525 1526 1528 1531 1533 1535 1543 1555 1556 1560 1562 1569 1570 1571 1574 1577 1578 1579 1580 1581 1582 1584 1585 1588 1590 1591 1592 1595 1596 1600 1608 1611 1612 1613 1616 1623 1624 1625 1627 1631 1632 1633 1635 1636 1637 1638 1639 1640 1641 1642 1643 1645 1647 1649 1653 1654 1655 1657 1660 1664 1665 1670 1671 1673 1675 1676 1678 1680 1681 1682 1684 1687 1691 1692 1695 1705 1710 1713 1722 1723 1725 1726 1727 1742 1748 1753 1755 1759 1764 1768 1770 1771 1773 1774 1775 1778 1781 1784 1785 1792 1793 1799 1807 1809 1810 1813 1818 1820 1824 1826 1828 1829 1831 1834 1835 1836 1837 1838 1846 1851 1853 1861 1868 1871 1873 1876 1880 1882 1883 1884 1886 1889 1890 1891 1899 1900 1906 1910 1912 1916 1917 1918 1921 1927 1930 1932 1947 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#nb_lw <- nb2listw(nb, style = 'W', zero.policy = TRUE)
#summary(nb_lw)
#lm.morantest(HDB.mlr, nb_lw)

The Global Moran’s I test for residual spatial autocorrelation shows that it’s p-value is less than 2.2e-16 which is less than the alpha value of 0.05. Hence, the null hypothesis can be rejected that the residuals are randomly distributed.

Since the Observed Global Moran I = 0.143 which is greater than 0, it can be inferred that the residuals resemble cluster distribution.

7.0 GWmodel

7.1 Building Fixed Bandwidth GWR Model

7.1.1 Computing fixed bandwith

The code chunk below to calibrate the gwr model using fixed bandwidth and gaussian kernel.

bw.fixed <- bw.gwr(formula = resale_price ~ floor_area_sqm+remaining_lease+Prox_supermarket+Prox_hawker+Prox_childcare+Prox_MRT_LRT+Freq_supermarket+Freq_hawker+Freq_childcare,data=HDB_resale.sp, approach="CV", kernel="gaussian", adaptive=FALSE, longlat=FALSE)
Take a cup of tea and have a break, it will take a few minutes.
          -----A kind suggestion from GWmodel development group
Fixed bandwidth: 14893798 CV score: 1.782486e+14 
Fixed bandwidth: 9206714 CV score: 1.779853e+14 
Fixed bandwidth: 5691903 CV score: 1.779826e+14 
Fixed bandwidth: 3519630 CV score: 1.779596e+14 
Fixed bandwidth: 2177092 CV score: 1.776228e+14 
Fixed bandwidth: 1347358 CV score: 1.779311e+14 
Fixed bandwidth: 2689896 CV score: 1.779943e+14 
Fixed bandwidth: 1860162 CV score: 1.779313e+14 
Fixed bandwidth: 2372966 CV score: 1.779263e+14 
Fixed bandwidth: 2056035 CV score: 1.779314e+14 
Fixed bandwidth: 2251909 CV score: 1.778409e+14 
Fixed bandwidth: 2130852 CV score: 1.779462e+14 
Fixed bandwidth: 2205669 CV score: 1.778941e+14 
Fixed bandwidth: 2159430 CV score: 1.778408e+14 
Fixed bandwidth: 2188008 CV score: 1.776371e+14 
Fixed bandwidth: 2170346 CV score: 1.779429e+14 
Fixed bandwidth: 2181261 CV score: 1.778332e+14 
Fixed bandwidth: 2174515 CV score: 1.776581e+14 
Fixed bandwidth: 2178684 CV score: 1.77695e+14 
Fixed bandwidth: 2176108 CV score: 1.779188e+14 
Fixed bandwidth: 2177700 CV score: 1.778148e+14 
Fixed bandwidth: 2176716 CV score: 1.780412e+14 
Fixed bandwidth: 2177324 CV score: 1.778478e+14 
Fixed bandwidth: 2176948 CV score: 1.778487e+14 
Fixed bandwidth: 2177181 CV score: 1.779286e+14 
Fixed bandwidth: 2177037 CV score: 1.776195e+14 
Fixed bandwidth: 2177003 CV score: 1.778936e+14 
Fixed bandwidth: 2177058 CV score: 1.776548e+14 
Fixed bandwidth: 2177024 CV score: 1.776195e+14 
Fixed bandwidth: 2177016 CV score: 1.776195e+14 
Fixed bandwidth: 2177011 CV score: 1.777483e+14 
Fixed bandwidth: 2177019 CV score: 1.776195e+14 
Fixed bandwidth: 2177014 CV score: 1.776195e+14 
Fixed bandwidth: 2177013 CV score: 1.776195e+14 
Fixed bandwidth: 2177012 CV score: 1.776195e+14 
Fixed bandwidth: 2177012 CV score: 1.777483e+14 
Fixed bandwidth: 2177013 CV score: 1.776195e+14 
Fixed bandwidth: 2177012 CV score: 1.776195e+14 
Fixed bandwidth: 2177012 CV score: 1.776195e+14 
Fixed bandwidth: 2177012 CV score: 1.776195e+14 
Fixed bandwidth: 2177012 CV score: 1.776195e+14 
Fixed bandwidth: 2177012 CV score: 1.776195e+14 
Fixed bandwidth: 2177012 CV score: 1.776195e+14 
Fixed bandwidth: 2177012 CV score: 1.776195e+14 
Fixed bandwidth: 2177012 CV score: 1.777483e+14 
Fixed bandwidth: 2177012 CV score: 1.776195e+14 
Fixed bandwidth: 2177012 CV score: 1.776195e+14 
Fixed bandwidth: 2177012 CV score: 1.777483e+14 
Fixed bandwidth: 2177012 CV score: 1.776195e+14 
Fixed bandwidth: 2177012 CV score: 1.776195e+14 
Fixed bandwidth: 2177012 CV score: 1.776195e+14 
Fixed bandwidth: 2177012 CV score: 1.776195e+14 
Fixed bandwidth: 2177012 CV score: 1.776195e+14 
Fixed bandwidth: 2177012 CV score: 1.776195e+14 
Fixed bandwidth: 2177012 CV score: 1.776195e+14 
Fixed bandwidth: 2177012 CV score: 1.776195e+14 

7.1.2 Calibrating GWR model

gwr.fixed <- gwr.basic(formula = resale_price ~ floor_area_sqm+remaining_lease+Prox_supermarket+Prox_hawker+Prox_childcare+Prox_MRT_LRT+Freq_supermarket+Freq_hawker+Freq_childcare,data=HDB_resale.sp, bw=bw.fixed, kernel = 'gaussian', longlat = FALSE)
gwr.fixed
   ***********************************************************************
   *                       Package   GWmodel                             *
   ***********************************************************************
   Program starts at: 2021-11-08 23:26:48 
   Call:
   gwr.basic(formula = resale_price ~ floor_area_sqm + remaining_lease + 
    Prox_supermarket + Prox_hawker + Prox_childcare + Prox_MRT_LRT + 
    Freq_supermarket + Freq_hawker + Freq_childcare, data = HDB_resale.sp, 
    bw = bw.fixed, kernel = "gaussian", longlat = FALSE)

   Dependent (y) variable:  resale_price
   Independent variables:  floor_area_sqm remaining_lease Prox_supermarket Prox_hawker Prox_childcare Prox_MRT_LRT Freq_supermarket Freq_hawker Freq_childcare
   Number of data points: 15888
   ***********************************************************************
   *                    Results of Global Regression                     *
   ***********************************************************************

   Call:
    lm(formula = formula, data = data)

   Residuals:
    Min      1Q  Median      3Q     Max 
-206108  -72186  -27206   40382  712943 

   Coefficients:
                     Estimate Std. Error t value Pr(>|t|)    
   (Intercept)      86145.655  15292.055   5.633 1.80e-08 ***
   floor_area_sqm     812.367    122.949   6.607 4.04e-11 ***
   remaining_lease   3585.982     68.847  52.087  < 2e-16 ***
   Prox_supermarket   -38.222      9.252  -4.131 3.63e-05 ***
   Prox_hawker         10.509      3.461   3.036  0.00240 ** 
   Prox_childcare      74.985      9.869   7.598 3.17e-14 ***
   Prox_MRT_LRT       -47.272      4.117 -11.481  < 2e-16 ***
   Freq_supermarket  2082.758    680.960   3.059  0.00223 ** 
   Freq_hawker      39946.605   1341.389  29.780  < 2e-16 ***
   Freq_childcare   -2503.516    192.347 -13.016  < 2e-16 ***

   ---Significance stars
   Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
   Residual standard error: 106200 on 15878 degrees of freedom
   Multiple R-squared: 0.2193
   Adjusted R-squared: 0.2189 
   F-statistic: 495.7 on 9 and 15878 DF,  p-value: < 2.2e-16 
   ***Extra Diagnostic information
   Residual sum of squares: 1.790816e+14
   Sigma(hat): 106174
   AIC:  412846.6
   AICc:  412846.6
   BIC:  397149.4
   ***********************************************************************
   *          Results of Geographically Weighted Regression              *
   ***********************************************************************

   *********************Model calibration information*********************
   Kernel function: gaussian 
   Fixed bandwidth: 2177012 
   Regression points: the same locations as observations are used.
   Distance metric: Euclidean distance metric is used.

   ****************Summary of GWR coefficient estimates:******************
                           Min.     1st Qu.      Median     3rd Qu.
   Intercept        -9.9472e+04 -9.9470e+04  1.8944e+05  1.8944e+05
   floor_area_sqm   -1.1872e+02 -1.1872e+02 -1.1872e+02  2.4090e+03
   remaining_lease   3.3352e+03  3.3352e+03  3.3352e+03  4.2286e+03
   Prox_supermarket -4.2268e+01 -4.2268e+01 -3.8147e-05 -3.8147e-05
   Prox_hawker      -3.0518e-05 -3.0518e-05 -3.0518e-05  5.5120e+00
   Prox_childcare    6.4850e-05  6.4850e-05  6.4850e-05  3.3010e+01
   Prox_MRT_LRT     -5.0855e+01 -5.0855e+01 -9.1553e-05 -9.1553e-05
   Freq_supermarket  1.3031e+03  1.3031e+03  1.3031e+03  2.1465e+03
   Freq_hawker       3.6049e+04  3.6049e+04  3.6049e+04  4.0958e+04
   Freq_childcare   -2.7239e+03 -2.7239e+03 -2.7087e+03 -2.7087e+03
                           Max.
   Intercept        189440.0000
   floor_area_sqm     2409.0838
   remaining_lease    4228.6728
   Prox_supermarket      0.0000
   Prox_hawker           5.5122
   Prox_childcare       33.0108
   Prox_MRT_LRT         -0.0001
   Freq_supermarket   2146.6439
   Freq_hawker       40957.9638
   Freq_childcare    -2708.6916
   ************************Diagnostic information*************************
   Number of data points: 15888 
   Effective number of parameters (2trace(S) - trace(S'S)): 13.0003 
   Effective degrees of freedom (n-2trace(S) + trace(S'S)): 15875 
   AICc (GWR book, Fotheringham, et al. 2002, p. 61, eq 2.33): 412729.8 
   AIC (GWR book, Fotheringham, et al. 2002,GWR p. 96, eq. 4.22): 412714.8 
   BIC (GWR book, Fotheringham, et al. 2002,GWR p. 61, eq. 2.34): 396939.6 
   Residual sum of squares: 1.777027e+14 
   R-square value:  0.225359 
   Adjusted R-square value:  0.2247246 

   ***********************************************************************
   Program stops at: 2021-11-08 23:28:29